The generator matrix

 1  0  1  1  1 14  1  1  0 14  1  1  1  0  1  2  1  1  1  8  1  1  1  8  1  6  1 10  1  1  1 14  1  4  1  1  0  1  0  1  1  0  6  1  1  1  1 12  1  1  1  1
 0  1 11  6  1  1  8  3  1  1 14  9  6  1  3  1 13  0  3  1  8 10  9  1 15  1 14  1 12 13 11  1 10  1 11  9  1 11  1  6  2  2  1  4  7 12  2  1 13 13  8  0
 0  0 12  0  0  0  0  8 12  4  4  4 12 12  0  4  8  8 12  8  4  4  4  0  0  4  0  8  4 12  0  8 12  4 12  8  0  4 12  8 12  0  8  0  4  0  8  8 12  4  0  0
 0  0  0 12  0  0  8  8  8  8  0  8  8 12 12 12 12 12 12 12 12 12  4  4  4  8  0  0 12  0  4 12  0  8 12  0 12  4  4  4 12  8  4 12  0 12  0 12 12 12  0  4
 0  0  0  0  4 12 12  8  4  0  0  4  4  8 12  4  0  4 12  4 12  8  0  0  4 12 12  0  8  8  0 12 12  0  8  8  4 12  8 12  4 12  0  8 12 12  8  0 12 12 12  4

generates a code of length 52 over Z16 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+34x^45+147x^46+318x^47+839x^48+1248x^49+1925x^50+2516x^51+2386x^52+2576x^53+2014x^54+1152x^55+702x^56+260x^57+116x^58+46x^59+31x^60+22x^61+16x^62+14x^63+8x^64+4x^65+5x^66+2x^67+1x^68+1x^70

The gray image is a code over GF(2) with n=416, k=14 and d=180.
This code was found by Heurico 1.16 in 2.79 seconds.